## Syllabus of Mathematics

## (For Final and International Round)

- Addition with 1-digit numbers without carrying
- Subtraction on 1-digit numbers without carrying
- Balance Problem
- Basic number pattern and figure pattern
- Odd and Even numbers
- Counting 2-D and 3-D shapes
- Arranging the number in order
- Creating 3 digit numbers
- Comparing numbers
- Matching Equation
- Counting numbers of sides and interior angles
- Basic Number sequence

- Basic number pattern and sequence
- Age and Date problem
- Addition 2 digits with carrying
- Subtraction 2 digits with carrying
- Odd and Even
- Counting on 2D and 3Dshapes
- Basic Arithmetic pattern
- Simple Combination
- Finding squares and triangles
- Balance problem
- Counting on numbers of sides and angles
- Formation of 3-digit numbers

- Addition and subtraction 3 digits with carrying
- Sum, different and multiples of number sentence
- IQ age problem and date problem
- Pigeonhole problem
- Basic concept about area and perimeter
- Guess on 3 digits numbers
- Chicken and rabbit theorem
- Counting on numbers of 2 D shapes
- Counting on the number of Vertices, Faces and Edges of 3-D figure
- Finding lines segments and intersection point
- Basic routing problem
- L.C.M and H.C.F

- Chicken and rabbit problem
- Pigeon Hole problem
- Speed and Time problem
- Calculation with decimal and fraction
- Area and perimeter of 2D shapes
- Excess and shortage problems
- Finding volume and surface area of 3D shapes
- Sum of positive numbers series
- Combinations and permutation
- Basic probability
- Method of difference equation
- Guess on 4 digits numbers

- Speed, distance and time problems
- Algebraic expression
- Basic Inequalities
- Pigeonhole theorem (Hard)
- Routing problem (Hard)
- Linear equation
- Volume and surface area of 3D shapes
- Factor theorem
- Distributions (Hard)
- Combination and permutations
- Counting on possible solution on Indefinite equations
- Pythagorean Theorem

- Four arithmetical operations on rational numbers and irrational numbers; HCF, LCM, square roots, cube roots, primes, prime factorization and relatively prime
- Length, mass, volume, time, money; percentage (including simple and compound interest formulae), ratio, rate, distance, speed, map scales, direct and inverse proportions
- Expansion and factorization of algebraic expressions; three perfect squares identities; linear and quadratic expressions, equations (including quadratic formula) and inequalities; solving word problems using algebra
- Graphs of linear (including distance-time and speed-time graphs, and gradient of straight line), quadratic and power functions (
*y*=*a xn*for*n*= –2, –1, 0, 1, 2, 3) - Standard form, indices (including zero, negative and fractional indices) and surds (including rationalizing denominator)
- Remainder and factor theorems; solving of cubic equations by factorization; two perfect cubes identities (i.e. sum and difference of perfect cubes); partial fractions; binomial theorem
- Properties of rectangle, square, triangle, parallelogram, rhombus, trapezium, kite and regular polygons; perpendicular bisector and angle bisector; exterior angle of triangle, sum of interior angles of polygon and sum of exterior angles of polygon; angles associated with parallel lines (corresponding angles, alternate angles and interior angles)
- Congruence tests for triangles, Area and perimeter of triangle, rectangle, square, parallelogram and trapezium;
- Probability of single events
- Circumference of circle; volume and surface area of prism, cylinder, pyramid, cone and sphere; arc length, sector area and area of segment of circle (where angles are in degrees and in radians)
- Pythagoras’ theorem and its converse; and generalized Pythagoras’ theorem
- Trigonometric ratios of acute and obtuse angles; sine rule; cosine rule; 3D problems
- Picture graphs (or pictograms), bar graphs, tables of values, line graphs, pie charts, histograms for ungroupped and grouped data; average (mean, median and mode)
- Simple Venn diagrams
- Divisibility tests and combined divisibility tests
- Number sequences and patterns (including formula to find 1 + 2 + 3 + … +
*n*, i.e. (𝑛+1)2, and formula for general term of arithmetic progression, i.e.*Tn*=*a*+ (*n*– 1)*d*, although students can use other methods) - Counting (e.g. no. of terminal zeros)
- Logarithms
- Derivative and Integrals
- Logic problems and Cryptarithms

- Four arithmetical operations on rational numbers and irrational numbers; HCF, LCM, square roots, cube roots, primes, prime factorization and relatively prime
- Length, mass, volume, time, money; percentage (including simple and compound interest formulae), ratio, rate, distance, speed, map scales, direct and inverse proportions
- Expansion and factorization of algebraic expressions; three perfect squares identities; linear and quadratic expressions, equations (including quadratic formula) and inequalities; solving word problems using algebra; modulus functions (excluding graphs)
- Graphs of linear (including distance-time and speed-time graphs), quadratic and power functions (
*y*=*a xn*for*n*= –2, –1, 0, 1, 2, 3) - Coordinate geometry formulae (gradient, length of line segment, midpoint, perpendicular lines, and shoelace formula)
- Standard form, indices (including zero, negative and fractional indices) and surds (including rationalizing denominator); logarithms (including product law, quotient law, power law and change of base formula)
- Remainder and factor theorems; solving of cubic equations by factorization; two perfect cubes identities (i.e. sum and difference of perfect cubes); partial fractions; binomial theorem
- Properties of rectangle, square, triangle, parallelogram, rhombus, trapezium, kite and regular polygons; perpendicular bisector and angle bisector
- Exterior angle of triangle, sum of interior angles of polygon and sum of exterior angles of polygon; angles associated with parallel lines (corresponding angles, alternate angles and interior angles)
- Symmetric and angle properties of circles
- Congruence and similarity tests for triangles
- Area and perimeter of triangle, rectangle, square, parallelogram and trapezium; area and
- Circumference of circle; volume and surface area of prism, cylinder, pyramid, cone and sphere; arc length, sector area and area of segment of circle (where angles are in degrees and in radians)
- Pythagoras’ theorem and its converse; and generalized Pythagoras’ theorem
- Trigonometric ratios of angles in all quadrants; sine rule; cosine rule; 3D problems; angle of elevation, angle of depression and bearings; graphs of sine, cosine and tangent functions; cosecant, secant and cotangent; trigonometric identities, formulae and equations
- Picture graphs (or pictograms), bar graphs, tables of values, line graphs, pie charts, histograms for ungroupped and grouped data; average (mean, median and mode)
- Probability of single and combined events (including additive law for mutually exclusive events, multiplicative law for independent events, possibility diagrams, tree diagrams and probability trees for independent and dependent events; but excluding non-mutually exclusive events and
- Bayes’ theorem (for conditional probabilities)
- Divisibility tests and combined divisibility tests
- Number sequences and patterns (including formula to find 1 + 2 + 3 + … +
*n*, i.e. (𝑛+1)2, and formula for general term of arithmetic progression, i.e.*Tn*=*a*+ (*n*– 1)*d*, although students can use other methods) - Counting (e.g. no. of terminal zeros)
- Simple Venn diagrams
- Logarithms, Derivative and Integrals
- Logic problems and Cryptarithms